Nonlinear Dynamical System Model for Drive Mode Amplitude Instabilities in MEMS Gyroscopes

The requirements pertaining to the reliability and accuracy of micro-electromechanical gyroscopic sensors are increasing, as systems for vehicle localization emerge as an enabling factor for autonomous driving. Since micro-electromechanical systems (MEMS) became a mature technology, the modelling techniques used for predicting their behaviour expanded from mostly linear approaches to include nonlinear dynamic effects. This leads to an increased understanding of the various nonlinear phenomena that limit the performance of MEMS sensors. In this work, we develop a model of two nonlinearly coupled mechanical modes and employ it to explain measured drive mode instabilities in MEMS gyroscopes. Due to 3:1 internal resonance between the drive mode and a parasitic mode, energy transfer within the conservative system occurs. From measurements of amplitude response curves showing hysteresis effects, we extract all nonlinear system parameters and conclude that the steady-state model needs to be expanded by a transient simulation in order to fully explain the measured system behaviour.